Statistical Inference and Synthesis in the Image Domain for Mobile Robot Environment Modeling L. Abril Torres-Méndez and Gregory Dudek Centre for Intelligent Machines School of Computer Science McGill University

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Outline Introduction Problem statement Overview of the method Related work Range Synthesis Algorithm Experimental results Conclusions and future directions

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Our Application Automatic generation of 3D maps. Robot navigation, localization - Ex. For rescue and inspection tasks. Robots are commonly equipped with camera(s) and laser rangefinder.  Would like a full range map of the the environment.  Simple acquisition of data

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Problem Context Pure vision-based methods –Shape-from-X remains challenging, especially in unconstrained environments. Laser line scanners are commonplace, but –Volume scanners remain exotic, costly, slow. –Incomplete range maps are far easier to obtain that complete ones. Proposed solution: Combine visual and partial depth Shape-from-(partial) Shape

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Problem Statement From incomplete range data combined with intensity, perform scene recovery. From range scans like this infer the rest of the map

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Overview of the Method Approximate the composite of intensity and range data at each point as a Markov process. Infer complete range maps by estimating joint statistics of observed range and intensity.

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems What knowledge does Intensity provide about Surfaces? Two examples of kind of inferences: Intensity image Range image surface smoothness variations in depth surface smoothness far close

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems What about outliers? Changes in intensity from texture-like regions Intensity Range Not critical for reconstruction since very close neighborhoods represent the same type of smooth surface.

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems What about Edges? Edges often detect depth discontinuities Very useful in the reconstruction process! Intensity Range edges

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Range synthesis basis Range and intensity images are correlated, in complicated ways, exhibiting useful structure. - Basis of shape from shading & shape from darkness, but they are based on strong assumptions. The variations of pixels in the intensity and range images are related to the values elsewhere in the image(s). Markov Random Fields

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Related Work Probabilistic updating has been used for –image restoration [e.g. Geman & Geman, TPAMI 1984] as well as –texture synthesis [e.g. Efros & Leung, ICCV 1999]. Problems: Pure extrapolation/interpolation: –is suitable only for textures with a stationary distribution –can converge to inappropriate dynamic equilibria

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems MRFs for Range Synthesis States are described as augmented voxels V=(I,R,E). Z m =(x,y):1≤x,y≤m Z m =(x,y):1≤x,y≤m: mxm lattice over which the image are described. I = {I x,y }, (x,y)  Z m I = {I x,y }, (x,y)  Z m : intensity (gray or color) of the input image E is a binary matrix (1 if an edge exists and 0 otherwise). R={R x,y }, (x,y)  Z m R={R x,y }, (x,y)  Z m : incomplete depth values We model V as an MRF. I and R are random variables. R I v x,y Augmented Range Map I R

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Markov Random Field Model Definition: A stochastic process for which a voxel value is predicted by its neighborhood in range and intensity. N x,y is a square neighborhood of size n x n centered at voxel V x,y.

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Computing the Markov Model From observed data, we can explicitly compute intensity intensity & range V x,y N x,y This can be represented parametrically or via a table. –To make it efficient, we use the sample data itself as a table.

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems ­ Further, we can do this even with partial neighborhood information. Estimation using the Markov Model From what should an unknown range value be? ¬For an unknown range value with a known neighborhood, we can select the maximum likelihood estimate for V x,y. ® Even further, if both intensity and range are missing we can marginalize out the unknown neighbors. intensity intensity & range

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Interpolate PDF In general, we cannot uniquely solve the desired neighborhood configuration, instead assume The values in N u,v are similar to the values in N x,y, (x,y) ≠ (u,v). Similarity measure: Similarity measure: Gaussian-weighted SSD ( sum of squared differences ). Update schedule is purely causal and deterministic.

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Order of Reconstruction Dramatically reflects the quality of the result. Our reconstruction sequence is based on the amount of reliable information surrounding each of the voxels to be synthesized. Edge information used to defer reconstruction of voxels with edges as much as possible. Info-edge-driven ordering Correct result With the spiral-ordering

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Experimental Evaluation Obtain full range and intensity maps of the same environment. Remove most of the range data, then try and estimate what it is. Use the original ground truth data to estimate accuracy of the reconstruction.

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Arbitrary shape of unknown range data Input Intensity Synthesized result Scharstein & Szeliski’s Data Set Middlebury College Compact case Ground truth range Input range image Synthesized result Ground truth range

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Input IntensityGround truth range Input range image Arbitrary shape of unknown range data Scharstein & Szeliski’s Data Set Middlebury College Less compact case Synthesized result

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Arbitrary shape of unknown range data Compact Distributed Synthesized results Ground truth range Expected quality of reconstruction degrades with distance from known boundaries Need broader distribution of range-intensity combinations in the sampling

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Ground truth range Approximated scene size: 550cms. Type I: Stripes along the x- and y-axis Input Intensity Data courtesy of Oak Ridge National Labs & Univ. of Florida xwxw rwrw Case 1: r w =10, x w =20. 39% of missing range Synthesized Result Mean Absolute Residual (MAR) Error: 5.76 cms. Ground truth range Approximated scene size: 550cms.

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Initial range (r w =5, x w =25). 61% of missing range Case 2 Result Input intensity Mean Absolute Residual (MAR) Error: 8.86 cms. Initial range 61% missing range Ground truth range (approx. scene size: 550 cms.)

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Case 3 Result Initial range 76% missing range Input intensity Initial range data (r w =3, x w =28). 76% missing range Mean Absolute Residual (MAR) Error: 9.99 cms. Ground truth range (approx. scene size: 550 cms.)

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Input intensity and range data Synthesized results Ground truth range

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Input range data. 66% of missing range Achromatic vs. Color Results Using achromatic image Using color image Synthesized range images Greyscale image Color image Ground truth range

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Type II: Stripes along the x-axis (like those obtained by our robot) Case 1: r w =10, x w = % of missing range xwxw rwrw xwxw rwrw Input Intensity Ground truth range Approx. scene size: 600cms. Synthesized Result MAR Error: cms. Ground truth range Approximated scene size: 600cms.

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Case 2 Result Mean Absolute Residual (MAR) Error: cms. 75% missing rangeInput intensity

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Case 3 Result Mean Absolute Residual (MAR) Error: cms. 78% missing rangeInput intensity

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Mike, just in case somebody ask The picture on the top appears on the paper and the bottom one on this presentation. The only difference is in the region indicated by the red ellipse in the ground truth range image (right). This region corresponds to the glass window of the intensity image (left). Because it is a reflective surface, our laser range finder cannot measure it correctly. We decided to inter- polate all the incorrect measure- ments to get a new ground truth range image (bottom). Thus, the synthesized images also differ.

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems More Experimental Results

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Conclusions Works very well -- is this consistent? Can be more robust than standard methods (e.g. shape from shading) due to limited dependence on a priori reflectance assumptions. Depends on adequate amount of reliable range as input. Depends on statistical consistency of region to be constructed and region that has been measured.

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Discussion & Ongoing Work Surface normals are needed when the input range data do not capture the underlying structure Data from real robot –Issues: non-uniform scale, registration, correlation on different type of data –Integration of data from different viewpoints

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Questions ?

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Adding Surface Normals Not in the paper We compute the normals by fitting a plane (smooth surface) in windows of n x n pixels. Normal vector: Eigenvector with the smallest eigenvalue of the covariance matrix. Similarity is now computed between surface normals instead of range values.

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Initial range scans Preliminary Results Not in the paper Synthesized range image Ground truth range Edge map Real intensity image Initial range data Real intensity imageEdge map

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems The Neighborhood The neighborhood N {x,y} is a square mask of size nxn centered at the augmented voxel. Observations: The neighborhood is causal The size is important to capture relevant characteristics v (x,y) I R Neighborhood of v (x,y) N {x,y}

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems

Initial range (none) Novel View Synthesis (ongoing work) Intensity image Range image Known intensity image Infer range map from intensity of current view and from range and intensity of other views. Other view Current view to estimate range map Synthesized range Ground truth range

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Previous results Results using EDGES Ground truth range MAR Errors (cms.)

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems More examples Synthesized results Ground truth rangeThe input intensity and range data

2004 IEEE/RSJ International Conference on Intelligent Robots and Systems Adding Surface Normals Not in the paper We compute the normals by fitting a plane (smooth surface) in windows of nxn pixels. The eigenvector with the smallest eigenvalue of the covariance matrix is the normal vector. – The smallest eigenvalue measures the quality of the fit. In the range synthesis, the similarity is now computed between surface normals instead of range values.